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The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of...

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by E=35ZZ-1e24πε0R The measured masses of the neutron, H11, O815 are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u respectively. Given that the radii of both the N715 and O815 nuclei are same, 1u = 931.5 Me V/ c2 (c is the speed of light) and e24πϵ0=1.44 MeV fm. Assuming that the difference between the binding energies of N715 and O815 is purely due to the electrostatic energy, the radius of either of the nuclei is 1 fm=10-15m
2.85 fm
3.03 fm
3.42 fm
3.80 fm
Solution:
Electrostatic energy =BEN-BEO
=7MH+8Mn-MN-8MH+7Mn-MO×C2
=-MH+Mn+MO-MNC2
=-1.007825+1.008665+15.003065-15.000109×931.5
=+3.5359 MeV
E=35×1.44×8×7R-35×1.44×7×6R=3.5359
R=3×1.44×145×3.5359=3.42 fm